A torque-vectoring differential (TVD), which is well known in the prior art, is an electronically controlled differential that can create an understeering or oversteering moment about the center of gravity of a motor vehicle independent of the speeds of the wheels so as to affect the dynamics of a vehicle, utilizing concepts of understeer and oversteer gradients that are well understood in the prior art. A TVD is different from a Limited Slip Differential (LSD) which generates understeer or oversteer moments as a function of the wheel speed difference across the LSD. Therefore, the ability of a TVD to create an understeering or oversteering moment about the center of gravity of a motor vehicle independent of the speeds of the wheels, up to a fixed limit of wheel speed difference, greatly increases the range of authority that a TVD has on vehicle dynamics, as compared with an LSD.
FIG. 1 is a schematic depiction of a motor vehicle 100 illustrating the operation of, for example, a torque vectoring differential 102 about the center of gravity 104 of the motor vehicle. The motor vehicle 100 has a track width (ie., wheelbase width) L. The left rear (LR) wheel torque 108 and the right rear (RR) wheel torque 110 generate a TVD yaw moment 112 about the center of gravity 104, via, for example a TVD 102, wherein arrow 114 designates the path of the motor vehicle 100.
In this regard, a delta torque, (LR Wheel Torque 108-RR Wheel Torque 110) output, generated by a variety of yaw rate controllers, which is well know in the prior art, is input to, for example, a TVD 102 to produce the yaw moment 112 generated about the center of gravity 104 of the motor vehicle 100, and can be expressed as:Yaw Moment=(LR Wheel Torque−RR Wheel Torque)·(L/(2(Tire Radius))),  (1)wherein the track width (wheelbase width) L and Tire Radius of the motor vehicle are known. The input to the various yaw rate controllers, as is well known in the prior art, are a desired vehicle yaw rate and measured vehicle yaw rate or a vehicle yaw rate error and a desired vehicle yaw acceleration (yaw rate commands) from which the yaw rate controller outputs the delta torque (i.e., LR Wheel Torque 108—RR Wheel Torque 110) to the TVD 102.
The methodology utilized by the prior art is an entirely empirical method, utilizing an empirical dual look-up table based methodology for generating desired yaw rate commands for use with a TVD. The method of the prior art requires extensive vehicle testing with physical hardware, requiring extended development time, is limited to producing yaw rates observed in the test regime, and requires a measurement of vehicle lateral acceleration. Furthermore, the prior art method generates a nonlinear vehicle response if a continuous variation of the understeer gradient is attempted. The method of the prior art is, therefore, unsatisfactory, since it does not consider true driver objectives and is dependent on actuator limitations.
Accordingly, what is needed in the art is a method for generating yaw rate commands for providing closed loop vehicle dynamic control with torque vectoring differentials.